The Old Trafford crowd serenaded United's players with "ole" late in Amorim's first Premier League game at Old Trafford.
It marks a big change from the boos that rang around the stadium toward the end of former manager Erik ten Hag's reign.
In Amorim's third game in charge, United produced their best performance under him yet, with Marcus Rashford and Joshua Zirkzee scoring two goals each.
Amorim is undefeated since taking over last month and United are now ninth - four points off the top four.
Goals from Nicolas Jackson, captain Enzo Fernandez and Cole Palmer earned Chelsea a 3-0 home win over Aston Villa lifting them to joint second in the table.
Senegal striker Jackson neatly side-footed a Marc Cucurella cross from the left, knocking it in off the post in the seventh minute.
Chelsea took advantage of questionable defending in the 36th minute when Fernandez was fed by Palmer before steadying himself and firing home.
Palmer then lofted an exquisite left-foot shot into the top corner of substitute goalkeeper Robin Olsen's net in the 83rd minute.
Chelsea's Enzo Fernandez celebrates after scoring his side's second goal against Aston Villa. (AP PHOTO)
Tottenham's hit and miss form continued under their Australian coach Ange Postecoglou after they were held to a 1-1 home draw a week after thrashing champions Manchester City 4-0.
Fulham captain Tom Cairney came off the bench to rescue a point before being sent off after Brennan Johnson's volley gave the hosts the lead.
The visitors weathered late pressure and held on for a deserved point, which put them 10th in the table with 19 points from 13 games.
Former Socceroos boss Spurs Postecoglou's Spurs, with only their second league draw this season, moved up to seventh with 20 points, three points behind fourth-placed Brighton.
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